1. Do you mean web on mobile or compiled into an android/iOS app? If it's web then yes. For mobile, I think you need to test what you want to do with the Intel XDK / phonegap (not sure about crosswalk) and as far as I know the clay plugin doesn't work with the cocoonjs plugin.
2. There's no need for 2 game versions because the clay.io plugin allows for in-game purchases. So, just have level 1 as your demo level (make it good!!) and then ask for payment to continue. I haven't read the documentation on how to implement these features but the manual on the clay.io website is quite comprehensive and should explain how to do this.
3. I think this will only be limited by your answer to 1 - what export to mobile option are you planning on?
4. Oh yes!!